Chiral SU(2) L × SU(2) R liquids: a theory of heavy nuclei and neutron stars

Abstract

The global SU(2) L × SU(2) R symmetries of QCD probably imply the existence of a liquid phase consisting of protons, neutrons and pions. Drops of this “chiral liquid” at zero external pressure emerge as saturating (the baryon number grows roughly as the volume) nontopological solitons of the low energy non-linear chiral effective lagrangian theory of pions and nucleons, where the pions are the pseudo-Goldstone bosons resulting from the spontaneous breaking of SU(2) L− R by the QCD vacuum. Chiral perturbation theory of linear SU(2) L+ R × non-linear SU(2) L− R gives us control of both the tree and quantum loop levels of the theory. A crucial role is played by explicit SU(2) L− R breaking terms whose origin lies in quark masses; an isosinglet combination of even numbers of pions carries the primary long-range attractive force. If non-linear chiral symmetry contains such saturating nontopological soliton field configurations, they would give a chiral-symmetric explanation for the existence of ordinary heavy nuclei, which are then to be regarded as just droplets of chiral liquid. This picture, reminiscent of the old liquid drop model of heavy nuclei, vastly simplifies the extraction of bulk nuclear properties from chiral symmetry; nucleons, treated as Fermi fluids inside a heavy nucleus, move within a huge coherent self-consistent classical pion field 〈π 2〉 1 2 t~ 200–400 MeV . Neutron stars are then just great oceans of neutral chiral liquid held together by gravity. Quantum chiral liquids can have interesting macroscopic quantum properties such as the spontaneous breaking of parity with parity doubling; these may distinguish experimentally the chiral liquid theory of heavy nuclei and neutron stars from more conventional models.